Showing papers by "Oliver Kosut published in 2022"

Grid Topology Identification With Hidden Nodes via Structured Norm Minimization

Abstract: This letter studies a topology identification problem for an electric distribution grid using sign patterns of the inverse covariance matrix of bus voltage magnitudes and angles, while accounting for hidden buses. Assuming the grid topology is sparse and the number of hidden buses are fewer than those of the observed buses, we express the observed voltages inverse covariance matrix as the sum of three structured matrices: sparse matrix, low-rank matrix with sparse factors , and low-rank matrix . Using the sign patterns of the first two of these matrices, we develop an algorithm to identify the topology of a distribution grid with a minimum cycle length greater than three. To estimate the structured matrices from the empirical inverse covariance matrix, we formulate a novel convex optimization problem with appropriate sparsity and structured norm constraints and solve it using an alternating minimization method. We validate the proposed algorithm’s performance on a modified IEEE 33 bus system.

The Saddle-Point Accountant for Differential Privacy

Abstract: We introduce a new differential privacy (DP) accountant called the saddle-point accountant (SPA). SPA approximates privacy guarantees for the composition of DP mechanisms in an accurate and fast manner. Our approach is inspired by the saddle-point method—a ubiquitous numerical technique in statistics. We prove rigorous performance guarantees by deriving upper and lower bounds for the approximation error offered by SPA. The crux of SPA is a combination of large-deviation methods with central limit theorems, which we derive via exponentially tilting the privacy loss random variables corresponding to the DP mechanisms. One key advantage of SPA is that it runs in constant time for the n -fold composition of a privacy mechanism. Numerical experiments demonstrate that SPA achieves comparable accuracy to state-of-the-art accounting methods with a faster runtime.

A Machine Learning Framework for Event Identification via Modal Analysis of PMU Data

Abstract: —Power systems are prone to a variety of events (e.g. line trips and generation loss) and real-time identification of such events is crucial in terms of situational awareness, reliability, and security. Using measurements from multiple synchrophasors, i.e., phasor measurement units (PMUs), we propose to identify events by extracting features based on modal dynamics. We combine such traditional physics-based feature extraction methods with machine learning to distinguish different event types. Including all measurement channels at each PMU allows exploiting diverse features but also requires learning classification models over a high-dimensional space. To address this issue, various feature selection methods are implemented to choose the best subset of features. Using the obtained subset of features, we investigate the performance of two well-known classification models, namely, logistic regression (LR) and support vector machines (SVM) to identify generation loss and line trip events in two datasets. The first dataset is obtained from simulated generation loss and line trip events in the Texas 2000-bus synthetic grid. The second is a proprietary dataset with labeled events obtained from a large utility in the USA involving measurements from nearly 500 PMUs. Our results indicate that the proposed framework is promising for identifying the two types of events.

A Variational Formula for Infinity-Rényi Divergence with Applications to Information Leakage

Abstract: We present a variational characterization for the Rényi divergence of order infinity. Our characterization is related´ to guessing: the objective functional is a ratio of maximal expected values of a gain function applied to the probability of correctly guessing an unknown random variable. An important aspect of our variational characterization is that it remains agnostic to the particular gain function considered, as long as it satisfies some regularity conditions. Also, we define two variants of a tunable measure of information leakage, the maximal αleakage, and obtain closed-form expressions for these information measures by leveraging our variational characterization.

An Operational Approach to Information Leakage via Generalized Gain Functions

Abstract: We introduce a gain function viewpoint of information leakage by proposing maximal g -leakage , a rich class of operationally meaningful leakage measures that subsumes recently introduced leakage measures maximal leakage and maximal α -leakage. In maximal g -leakage, the gain of an adversary in guessing an unknown random variable is measured using a gain function applied to the probability of correctly guessing. In particular, maximal g -leakage captures the multiplicative increase, upon observing Y , in the expected gain of an adversary in guessing a randomized function of X , maximized over all such randomized functions. We show that maximal leakage is an upper bound on maximal g -leakage, for any non-negative gain function g . We obtain a closed-form expression for maximal g -leakage for a class of concave gain functions. We also study two variants of maximal g -leakage depending on the type of an adversary and obtain closed-form expressions for them, which do not depend on the particular gain function considered as long as it satisfies some mild regularity conditions. We do this by developing a variational characterization for the R´enyi divergence of order infinity which naturally generalizes the definition of pointwise maximal leakage to incorporate arbitrary gain functions. Finally, we study information leakage in the scenario where an adversary can make multiple guesses by focusing on maximizing a specific gain function related to α -loss. In particular, we first completely characterize the minimal expected α -loss under multiple guesses and analyze how the corresponding leakage measure is affected with the number of guesses. We also show that a new measure of divergence that belongs to the class of Bregman divergences captures the relative performance of an arbitrary adversarial strategy with respect to an optimal strategy in minimizing the expected α -loss. leakage R´enyi divergence of orders. the setting which attempts in guessing by focusing on a specific tunable gain function. Such a has for log-loss (a special case of our tunable loss function) which extensively used machine There studied. We maximal g -leakage is equal to Sibson mutual information of order class of concave gain We new measure of divergence relative arbitrary adversarial strategy with minimizing One limitation of our that we reverse

Localization and Estimation of Unknown Forced Inputs: A Group LASSO Approach

Abstract: We model and study the problem of localizing a set of sparse forcing inputs for linear dynamical systems from noisy measurements when the initial state is unknown. This problem is of particular relevance to detecting forced oscillations in electric power networks. We express measurements as an additive model comprising the initial state and inputs grouped over time, both expanded in terms of the basis functions (i.e., impulse response coefficients). Using this model, with probabilistic guarantees, we recover the locations and simultaneously estimate the initial state and forcing inputs using a variant of the group LASSO (linear absolute shrinkage and selection operator) method. Specifically, we provide a tight upper bound on: (i) the probability that the group LASSO estimator wrongly identifies the source locations, and (ii) the $\ell_2$-norm of the estimation error. Our bounds explicitly depend upon the length of the measurement horizon, the noise statistics, the number of inputs and sensors, and the singular values of impulse response matrices. Our theoretical analysis is one of the first to provide a complete treatment for the group LASSO estimator for linear dynamical systems under input-to-output delay assumptions. Finally, we validate our results on synthetic models and the IEEE 68-bus, 16-machine system.

An Alphabet of Leakage Measures

Abstract: We introduce a family of information leakage measures called maximal α, β-leakage, parameterized by real numbers α and β. The measure is formalized via an operational definition involving an adversary guessing an unknown function of the data given the released data. We obtain a simple, computable expression for the measure and show that it satisfies several basic properties such as monotonicity in β for a fixed α, non-negativity, data processing inequalities, and additivity over independent releases. Finally, we highlight the relevance of this family by showing that it bridges several known leakage measures, including maximal α-leakage (β = 1), maximal leakage (α = ∞, β = 1), local differential privacy (α = ∞, β = ∞), and local Rényi differential privacy (α = β).

On the Benefit of Cooperation in Relay Networks

Abstract: This work addresses the cooperation facilitator (CF) model, in which network nodes coordinate through a rate limited communication device. For multiple-access channel (MAC) encoders, the CF model is known to show significant rate benefits, even when the rate of cooperation is negligible. Specifically, the benefit in MAC sum-rate, as a function of the cooperation rate CCF , sometimes has an infinite slope at CCF = 0 when the CF enables transmitter dependence where none was possible otherwise. This work asks whether cooperation through a CF can yield similar infinite-slope benefits when dependence among MAC transmitters has no benefit or when it can be established without the help of the CF. Specifically, this work studies the CF model when applied to relay nodes of a single-source, single-terminal, diamond network comprising a broadcast channel followed by a MAC. In the relay channel with orthogonal receiver components, careful generalization of the partial-decode-forward/compress-forward lower bound to the CF model yields sufficient conditions for an infinite-slope benefit. Additional results include derivation of a family of diamond networks for which the infinite-slope rate-benefit derives directly from the properties of the corresponding MAC studied in isolation.

A Complex-LASSO Approach for Localizing Forced Oscillations in Power Systems

Abstract: We study the problem of localizing multiple sources of forced oscillations (FOs) and estimating their characteristics, including frequency, phase, and amplitude, using noisy PMU data. We assume sparsity in the number of locations, and for each location, we model the input FO as a sum of a few unknown sinusoids. This allows us to obtain a sparse linear model in the frequency domain that relates measurements and the unknown input locations at frequencies of the unknown sinusoidal terms. We determine these frequencies by thresholding the empirical spectrum of the noisy data. Finally, we cast the location recovery problem as an $\ell_{1}$-regularized least squares problem in the complex domain-i.e., complex-LASSO (linear shrinkage and selection operator). We numerically solve this optimization problem using the complex-valued coordinate descent method and show its efficiency on the IEEE 68-bus, 16 machine and WECC 179-bus, 29-machine systems.

Cactus Mechanisms: Optimal Differential Privacy Mechanisms in the Large-Composition Regime

Abstract: Most differential privacy mechanisms are applied (i.e., composed) numerous times on sensitive data. We study the design of optimal differential privacy mechanisms in the limit of a large number of compositions. As a consequence of the law of large numbers, in this regime the best privacy mechanism is the one that minimizes the Kullback-Leibler divergence between the conditional output distributions of the mechanism given two different inputs. We formulate an optimization problem to minimize this divergence subject to a cost constraint on the noise. We first prove that additive mechanisms are optimal. Since the optimization problem is infinite dimensional, it cannot be solved directly; nevertheless, we quantize the problem to derive nearoptimal additive mechanisms that we call "cactus mechanisms" due to their shape. We show that our quantization approach can be arbitrarily close to an optimal mechanism. Surprisingly, for quadratic cost, the Gaussian mechanism is strictly suboptimal compared to this cactus mechanism. Finally, we provide numerical results which indicate that cactus mechanisms outperform Gaussian and Laplace mechanisms for a finite number of compositions.The full proofs can be found in the extended version at [1]. This paper is Part I in a pair of papers, where Part II is [2].

Parameter Estimation in Ill-conditioned Low-inertia Power Systems

Abstract: This paper examines model parameter estimation in dynamic power systems whose governing electro-mechanical equations are ill-conditioned or singular. This ill-conditioning is because of converter-interfaced power systems generators’ zero or small inertia contribution. Consequently, the overall system inertia decreases, resulting in low-inertia power systems. We show that the standard state-space model based on least squares or subspace estimators fails to exist for these models. We overcome this challenge by considering a least-squares estimator directly on the coupled swing-equation model but not on its transformed first-order state-space form. We specifically focus on estimating inertia (mechanical and virtual) and damping constants, although our method is general enough for estimating other parameters. Our theoretical analysis highlights the role of network topology on the parameter estimates of an individual generator. For generators with greater connectivity, estimation of the associated parameters is more susceptible to variations in other generator states. Furthermore, we numerically show that estimating the parameters by ignoring their ill-conditioning aspects yields highly unreliable results.

Robust Model Selection of Non Tree-Structured Gaussian Graphical Models

Abstract: We consider the problem of learning the structure underlying a Gaussian graphical model when the variables (or subsets thereof) are corrupted by independent noise. A recent line of work establishes that even for tree-structured graphical models, only partial structure recovery is possible and goes on to devise algorithms to identify the structure up to an (unavoidable) equivalence class of trees. We extend these results beyond trees and consider the model selection problem under noise for non tree-structured graphs, as tree graphs cannot model several real-world scenarios. Although unidentifiable, we show that, like the tree-structured graphs, the ambiguity is limited to an equivalence class. This limited ambiguity can help provide meaningful clustering information (even with noise), which is helpful in computer and social networks, protein-protein interaction networks, and power networks. Furthermore, we devise an algorithm based on a novel ancestral testing method for recovering the equivalence class. We complement these results with finite sample guarantees for the algorithm in the high-dimensional regime.